On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type

Gülden Gün Polat and Teoman Özer

Advances in Mathematical Physics, 2014, vol. 2014, issue 1

Abstract: In this study we apply partial Noether and λ‐symmetry approaches to a second‐order nonlinear autonomous equation of the form y′′ + f(y)y′ + g(y) = 0, called Liénard equation corresponding to some important problems in classical mechanics field with respect to f(y) and g(y) functions. As a first approach we utilize partial Lagrangians and partial Noether operators to obtain conserved forms of Liénard equation. Then, as a second approach, based on the λ‐symmetry method, we analyze λ‐symmetries for the case that λ‐function is in the form of λ(x, y, y′) = λ1(x, y)y′ + λ2(x, y). Finally, a classification problem for the conservation forms and invariant solutions are considered.

Date: 2014
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https://doi.org/10.1155/2014/107895

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:107895

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